Question

If H^-1(x) is the inverse of H(x), what is the value or H^-1(H(x))?

Answer 1

f(g(x))=ln(ex−1+1)=ln(ex)=xln(e)=x

Answer 2

Answer:

If H^-1(x) is the inverse of H(x) , then the value of the composition function:

    H^-1(H(x)) is:

              Option: D

               D.  x

Step-by-step explanation:

We know that the composition of a function and its inverse always gives us the resultant as identity function.

Here we have the function H(x) and its inverse function is represented by H^-1(x)

Then the composition:

     $H^{-1}H(x)=H(H^{-1}(x))=I(x)=x$

where I denotes the identity function.

                Hence, the correct answer is:  Option: D